Greece's parliament will be called to ratify the agreement after Macedonian lawmakers approve it, provided that Skopje fulfils preliminary European Union and North Atlantic Treaty Organisation requirements to begin membership talks, Kotzias said.
The two prime ministers are expected to sign the agreement over the next weekend.
"The name change will be implemented not only the country's global relations but also domestically", Tsipras said adding that Skopje would need to revise its constitution.
"This will set Skopje on its path to North Atlantic Treaty Organisation membership".
Macedonia will be named the Republic of North Macedonia, or Severna Makedonija in Macedonian, after reaching a deal with Greece on the decades-long name issue, Macedonian Prime Minister Zoran Zaev said.
Albanian Prime Minister Edi Rama called his Macedonian and Greek counterparts "two progressive leaders" and used their Twitter handles to give their praise, tweeting: "Balkans are today a better place thnx to you both".
Greece had objected to the name "Macedonia", fearing territorial claims on its eponymous northern region, as well as cultural appropriation of the Greek nature of Ancient Macedonia, a historically Greek province and important part of Ancient Greek history that has no direct connection between the modern citizens, who hail from a mixed Slavic heritage.
Greek Prime Minister Alexis Tsipras arrives for the swearing-in ceremony of his government at the Presidential Palace in Athens, Greece, September 23, 2015.
The name dispute has poisoned relations between the two countries since Macedonia's independence from Yugoslavia in 1991 and has prevented Macedonia from joining global institutions such as North Atlantic Treaty Organisation and the European Union.
They also urged the Council to endorse opening EU accession talks with Macedonia, which the European Commission recommended in April. Tusk said: "Thanks to you the impossible is becoming possible", he said.
Mr Tsipras said the deal dictates "a clear distinction between Greek Macedonia and our northern neighbours".
Greek Prime Minister Alexis Tsipras.
"We have a deal".
The EU's diplomatic chief Federica Mogherini said the deal "contributes to the transformation of the entire region of southeast Europe". He did not, however, spell out what the name will be. Tsipras had sought to protect Greece's region of Macedonia, birthplace of Alexander the Great, but the Greek coalition partner has vowed to vote against the proposed agreement.
The dispute has poisoned relations between the two neighbors since Macedonia's independence from Yugoslavia in 1991.
Mr Tsipras said the deal met the concerns of Greece that a revised name for Macedonia be a "compound" name with a geographical qualifier. It is now known formally at the United Nations under the interim name "Former Yugoslav Republic of Macedonia".
Organizers of past rallies in Greece's main cities against a compromise with Macedonia also expressed outrage at the deal, with one accusing Tsipras of "high treason".